I'm taking some long rides like London to Caernarfon, York to Edinburgh and so on. I find it more convenient to get to the station and buy a ticket right before leaving but am afraid they might say they're already booked out.

In my view, yes. I always book tickets in advance. But make sure to choose a reliable service, for example, you can check reviews here https://www.bookvipreviews.com/. Nowadays the internet is full of sites and scams so it would be great to check the info before. Hope it's useful.